Kenyan forces rescued "most" of the hostages held by terrorists in an upscale mall in Nairobi, after launching a "major assault" to put an end to the two-day long siege mounted by attackers who threw grenades and opened fire on unsuspecting crowds at an upscale mall in Nairobi, Kenyan police said.

"Most of the hostages have been rescued and security forces have taken control of most parts of the building," Kenyan police announced this afternoon.

The death toll from the attack at the Westgate Mall rose from 59 to 68 people as nine more bodies were recovered in the rescue mission, the Kenya Red Cross said in a message on its Twitter account.

Kenya's interior Cabinet secretary Joseph Lenku said at least 175 people were injured in the attack.

Five Americans are among the wounded, State Department Deputy Spokeswoman Marie Harf said in a statement.

There are currently no reports of any American casualties, Harf said. However, the Australian, British, Canadian, French, Ghanaian and Somali governments have acknowledged the deaths of their citizens, along with Kenyan nationals killed in the "despicable massacre of innocent men, women and children," she said.

Three British nationals are confirmed dead in the attack, as French and Canadian officials said that their nations each had two citizens killed.

While more than 1,000 people were rescued from the shopping center, at least 30 hostages remain trapped inside as Kenyan troops continue to swarm the mall area as a tense standoff ensues.

This morning, the first and second floor of Westgate Mall have been contained, as forces work to secure the ground floor and basement of the mall, a U.S. official told ABC News.

The gunmen appear to have been "contained" by responding forces, the official said. It is unclear if some of the attackers have escaped, the official said.

Terrified shoppers and staffers who were able to make their escape described a harrowing scene to Kenyan media, which involved stepping over dead bodies on the way to safety.

The gunmen hit one of the most upscale places in Nairobi.

The Westgate Mall is a destination for Kenya's elite. It bills itself as the city's premier mall, boasting that it offers customers a "first world interior" and a "safe and serene environment." It was opened in 2007 and has more than 80 stores.

Somalia's al-Qaidia-linked rebel group, al-Shabab, claimed responsibility for the attack, saying that it was in retaliation for the 2011 involvement of Kenyan forces in their country to fight the Islamic insurgents.

"They're seeking to embarrass Kenya and get them to withdraw their troops," Associated Press reporter Jason Straziuso, who is currently in Nairobi, told ABC News."These hardcore terrorists know that this generates news in Europe and America."

While Kenya's elite troops moved into position at the mall Saturday night, Straziuso said that the most important question now is how they plan to free the hostages who are held up inside.

The U.S. Embassy in Nairobi suspended all U.S government temporary personnel, and told Mission personnel to shelter in place, avoid the Westgate mall area and avoid demonstrations or gatherings as the situation, according to its Facebook page.

Harf said U.S. officials were closely monitoring the situation.

"We condemn this senseless act of violence that has resulted in death and injury for many innocent men, women, and children. Our condolences go out to the families and friends of all victims. We have reports of American citizens injured in the attack, and the U.S. Embassy is actively reaching out to provide assistance," Harf said in a statement.